According to University Faculty Rules final examinations must be given during final exam week, not during the last week of the quarter. See Rules of the University Faculty (http://trustees.osu.edu/rules8/index.php).
The schedule for final examinations is developed by the Associate Dean and announced soon after the beginning of each quarter. Each exam period lasts approximately two hours, and an attempt is made to minimize the likelihood of back‑to‑back exams for students and/or to allow a reasonable break between periods. Classes meet in their usual rooms for final examinations unless other arrangements are approved in advance. Instructors must not change the scheduled time for an examination without receiving approval in advance from the Associate Dean.